# Electrons in the Rutherford model [duplicate]

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I was reading about the Rutherford atomic model which said that electrons revolve around the nucleus the way the Earth and other planets revolve around the sun.

This model was,however,shunned as it did not accommodate the fact that when charged particles accelerate,they emit radiation,lose energy and fall into the nucleus.This does not happen in the case of the earth as it is electrically neutral.

But it does comprise charges.

So why don't the individual charges emit radiation ?

What difference does it make if the charges are moving alone or in vicinity of other charges?

How can charges differentiate if they are moving with or without charges?(Which would lead them to either emit or not emit radiation)

P.S- A simple answer would be appreciated as I am not familiar with Maxwell's theory of EM radiation.

## marked as duplicate by John Rennie, Chris♦, Jon Custer, stafusa, Kyle KanosMar 9 '18 at 11:07

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## 3 Answers

The electromagnetic effects of +/- charges in a moving neutral object cancel out.

Actually, the Earth emits gravitational waves which would cause it to spiral towards the Sun (if the Sun had constant mass, which it doesn't). This is what we see in black hole collisions.

In a real atom, each electron is effectively a cloud of charge and current, not changing in time. Think of water flowing smoothly over a rock, forming a stationary wave. If the flow is irregular, it will lead to waves spreading in all directions; but if it is perfectly smooth, it will not. The water flows, accelerates, and decelerates, but does not cause spreading waves.

Here is a more direct way to think about it. Electrons do not act like point charges in their orbitals. In fact, they act like a continuous distribution of charge and current that does not change with time. By analogy: Suppose you have a superconductive ring hanging in space, carrying a constant current. At each point in the ring, the electrons are accelerating because the direction of their motion is changing. But the distribution of current and charge is constant. That is why the ring will not radiate electromagnetic waves. However, if a single charged particle moved around a ring-shaped path it would radiate, because the distribution of current and charge in that case would not be constant.

It is incorrect to say that electrons move around the nucleus of an atom with constant velocity; they don't. The farther they are from the nucleus, the slower the effective velocity is; and the closer they are the faster it is. It's true that stationary charge/current distributions do not radiate, but "stationary" does not mean that nothing is going on: there is still a continuous distribution of what amounts to accelerating and decelerating charge motion. But because that distribution does not change in time, there is no radiation.

The bottom line answer to your question: A Rutherford atom, with point electrons orbiting a nucleus, would indeed radiate electromagnetic radiation. But Rutherford atoms do not exist.

Fact 1. Accelerated charged particles emit EM radiation (therefore loose energy) which means stationary charged particles or charged particles with constant velocity do not emit EM radiation.

Fact 2. Charged particles exert force on each other, attractive or repulsive depending on the sign of the charges (Coulomb's Law).

Fact 3. Force acting on a particle causes acceleration (Newton's Law).

So;

Q: why don't the individual charges emit radiation ?

A: Use Fact 1.

Q: What difference does it make if the charges are moving alone or in vicinity of other charges?

A: Use Facts 1 to 3.

Q: How can charges differentiate if they are moving with or without charges?(Which would lead them to either emit or not emit radiation)

A: Use Facts 2 & 3.

• @phhysicopath wrote: "Fact 1. Accelerated charged particles emit EM radiation (therefore loose energy) which means stationary charged particles or charged particles with constant velocity do not emit EM radiation." For that to explain why electrons in atons don't radiate, it is also necessary to show that electrons in atoms have constant velocity. But they do not have constant velocity. The correct answer is more subtle than that. – S. McGrew Mar 19 '18 at 18:42
• What really matters is that the effective charge density and momentum density are constant in time. No change -> no radiation. – S. McGrew Mar 19 '18 at 18:45